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Three Things Across the River (illustration)
FILE No.71Unsolved

Three Things Across the River

Difficulty ★☆☆about 5 minLogic PuzzleOrderConstraints
Dog, rabbit and carrot must cross a river. Left alone, the dog eats the rabbit and the rabbit eats the carrot.

Case Record

A hunter must take a dog, a rabbit and a carrot across a river. His boat holds himself plus just one item.

On a bank without the hunter, the dog and rabbit alone means the dog attacks the rabbit, and the rabbit and carrot alone means the rabbit eats the carrot. The dog and carrot alone are fine.

Each trip across the river counts as 1 crossing (in either direction).

Your question

What is the fewest number of crossings needed to get everything across safely?

Case Files

Evidence

Diagram

On a bank without the hunterPairResultDog + rabbitDog attacks rabbitRabbit + carrotRabbit eats carrotDog + carrotSafeThe first item to carry is the rabbit.
Diagram

Timeline

  1. Hunter and all three items on the near bank.
  2. Everything on the far bank.

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

Which item can be left behind first without trouble?

Open hint 2

After taking the dog over, can you leave the rabbit with it?

Open hint 3

Bringing something back is allowed.

Solve It

Your question

What is the fewest number of crossings needed to get everything across safely?

Choose the answer closest to the truth.

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The Truth

7

The answer is: 7 crossings.

1) Take the rabbit across. 2) Return alone. 3) Take the dog across. 4) Bring the rabbit back. 5) Take the carrot across. 6) Return alone. 7) Take the rabbit across.

Taking the rabbit first is the key; the dog and the carrot are safe together. The rabbit is brought back on crossing 4 so that it is never left alone with the dog or the carrot.

Number of boat trips1 Rabbit over. 2 Hunter back alone3 Dog over. 4 Rabbit back5 Carrot over. 6 Hunter back alone7 Rabbit over
Diagram of the solution

Key Points

  • List the dangerous pairs first
  • Decide what to carry first by elimination
  • Carrying something back can help

Why people get fooled

People assume cargo never comes back, so the "bring it back" move does not occur to them.

Similar tricks

  • The constraint-ordering type
  • The bring-it-back type

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